Left-right splitting of elliptic flow in heavy ion collisions: TRENTo-3D initialization and CLVisc hydrodynamic simulations

Using the TRENTo-3D initial condition model coupled with $(3+1)$-dimensional CLVisc hydrodynamic simulations, we systematically investigate the left-right splitting of elliptic flow $(\mathrm{\ensuremath{\Delta}}{v}_{2})$ for soft particles in relativistic heavy-ion collisions. Our study reveals that the final distribution characteristics of $\mathrm{\ensuremath{\Delta}}{v}_{2}$ primarily depend on the odd flow harmonics and ${v}_{2}$ itself. We find that the parton transverse momentum scale ${k}_{\text{T}}$ not only determines the geometric tilt of the QGP fireball but also significantly affects the rapidity dependence of both ${v}_{1}$ and $\mathrm{\ensuremath{\Delta}}{v}_{2}$, providing new insights into the splitting mechanism of $\mathrm{\ensuremath{\Delta}}{v}_{2}$. Furthermore, our results demonstrate that $\mathrm{\ensuremath{\Delta}}{v}_{2}({p}_{\text{T}})$ exhibits significant sensitivity to influences such as the subnucleonic degrees of freedom (or ``hotspots''), transverse momentum scale, and fragmentation region profile. By analyzing $\mathrm{\ensuremath{\Delta}}{v}_{2}$ and the $\mathrm{\ensuremath{\Delta}}{v}_{2}/{v}_{2}$ ratio, our findings provide new constraints on the uncertainties of the QGP initial state and provide additional constraints for refining model parameters.